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Cooperative Games: Core And Shapley Value

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  • Roberto Serrano

    ()
    (CEMFI, Centro de Estudios Monetarios y Financieros)

Abstract

This article describes the basic elements of the cooperative approach to game theory, one of the two counterparts of the discipline. After the presentation of some basic definitions, the focus will be on the core and the Shapley value, two of the most central solution concepts in cooperative game theory.

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File URL: http://www.cemfi.es/ftp/wp/0709.pdf
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Bibliographic Info

Paper provided by CEMFI in its series Working Papers with number wp2007_0709.

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Date of creation: Jul 2007
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Handle: RePEc:cmf:wpaper:wp2007_0709

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Keywords: Game theory; cooperative game; characteristic function; solution concept; core; Shapley value; axiomatics; equivalence principle; non-cooperative implementation.;

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References

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  1. Volij, Oscar & Serrano, Roberto, 1998. "Axiomatizations of Neoclassical Concepts for Economies," Staff General Research Papers 5192, Iowa State University, Department of Economics.
  2. Serrano Roberto, 1995. "A Market to Implement the Core," Journal of Economic Theory, Elsevier, vol. 67(1), pages 285-294, October.
  3. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
  4. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  5. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  6. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  7. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November.
  8. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
  9. Krishna, V. & Serrano, R., 1993. "Perfect Equilibria of a Model of N-Person Noncooperative Bargaining," Harvard Institute of Economic Research Working Papers 10, Harvard - Institute of Economic Research.
  10. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
  11. Geoffroy de Clippel & Hans Peters & Horst Zank, 2004. "Axiomatizing the Harsanyi solution, the symmetric egalitarian solution and the consistent solution for NTU-games," International Journal of Game Theory, Springer, vol. 33(1), pages 145-158, January.
  12. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  13. AUMANN, Robert J., . "Values of markets with a continuum of traders," CORE Discussion Papers RP -228, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Perez-Castrillo J. David, 1994. "Cooperative Outcomes through Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 428-440, November.
  15. Moldovanu Benny & Winter Eyal, 1995. "Order Independent Equilibria," Games and Economic Behavior, Elsevier, vol. 9(1), pages 21-34, April.
  16. Perry, M. & Rany, P., 1992. "A Non-Cooperative View of Coalition Formation and the Core," UWO Department of Economics Working Papers 9203, University of Western Ontario, Department of Economics.
  17. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
  18. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
  19. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  20. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  21. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  22. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer, vol. 4(2), pages 255-73, March.
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Citations

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Cited by:
  1. Roberto Serrano, 2004. "On Watson’s Non-Forcing Contracts and Renegotiation," Working Papers 2004-03, Brown University, Department of Economics.
  2. Roberto Serrano & Yusuke Kamishiro, 2009. "Equilibrium Blocking In Large Quasilinear Economies," Working Papers wp2009_0911, CEMFI.
  3. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.
  4. David Martinez-Miera & Rafael Repullo, 2010. "Does Competition Reduce the Risk of Bank Failure?," Review of Financial Studies, Society for Financial Studies, vol. 23(10), pages 3638-3664, October.
  5. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification?," CeMMAP working papers CWP24/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, And Debt Valuation," Working Papers wp2009_0902, CEMFI.
  7. Rafael Repullo & Javier Suarez, 2008. "The Procyclical Effects Of Basel Ii," Working Papers wp2008_0809, CEMFI.
  8. Joan Llull, 2008. "The Impact Of Immigration On Productivity," Working Papers wp2008_0802, CEMFI.

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